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Hunter-Best [27]

3 years ago

9

The prime factorization of a number is 3^2x5^3x7. Which statement is true about the factors of the number? ? Twenty-one is a fac

tor of the number because both 3 and 7 are prime factors. Twenty-one is not a factor of the number because 21 is not prime. Ninety is a factor of the number because 3^2=9 and 90 is divisible by 9. Ninety is not a factor of the number because 90 is not divisible by 7.

2 answers:

rodikova [14]3 years ago

7 0

The 1st statement is true.

21 is a factor because both 3 and 7 are factors.

olga_2 [115]3 years ago

6 0

Answer:

Twenty-one is a factor of the number because both 3 and 7 are prime factors.

Step-by-step explanation:

Given number is,

$3^2\times 5^3\times 7$

$=3\times 3\times 5\times 5\times 5\times 7$

Where, 3, 5 and 7 are prime numbers ( only divisible by 1 and itself ),

⇒ Both 3 and 7 are prime factors of the given number,

⇒ 21 is a factor of the given number.

Thus, first option is correct.

⇒ Second option is incorrect.

Now, 5 is factor of the given number but 2 is not,

⇒ 10 is not a factor of the given number,

⇒ 90 is not a factor of the given number,

⇒ Third option is incorrect.

Suppose 90 is divisible by 7,

⇒ 90 = 7a

Where a is any whole number,

⇒ $7=\frac{90}{a}$

$3^2\times 5^3\times 7=3^2\times 5^3\times \frac{90}{a}$

Since, 90 could be a factor of this number, if a = 3 or 5 or their multiple,

For the other values of a, 90 can not be the factor,

Hence, there is no effect of divisibility of 90 by 7 on having 90 as a factor of the given number,

⇒ Fourth option is incorrect.

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For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th

alexira [117]

Answer:

The inner function is $h(x)=4x^2 + 8$ and the outer function is $g(x)=3x^5$ .

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

Step-by-step explanation:

A composite function can be written as $g(h(x))$ , where $h$ and $g$ are basic functions.

For the function $f(x)=3(4x^2+8)^5$ .

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have $4x^2+8$ inside parentheses. So $h(x)=4x^2 + 8$ is the inner function and the outer function is $g(x)=3x^5$ .

The chain rule says:

$\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)$

It tells us how to differentiate composite functions.

The function $f(x)=3(4x^2+8)^5$ is the composition, $g(h(x))$ , of

outside function: $g(x)=3x^5$

inside function: $h(x)=4x^2 + 8$

The derivative of this is computed as

$\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4$

The derivative of the function is $\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4$ .

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Suzy has an Etsy store where she sells shirts. Her shirts come in five sizes: small, medium, large, extra-large, or 2XL. Her shi

Shalnov [3]

Answer:

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Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

It takes 52 minutes for 5 people to paint 5 walls.

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4 0

3 years ago

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antiseptic1488 [7]

The roots: this is when y=0, so in yours there are 2 roots. Just look at the x value when y=0 and that is your roots.

Y intercept- this is when x=0, so just look at the y value below x=0 and that is the y intercept. Note the answer will probably be in the form (0,_)

Vertex=do you see a pattern? Well the vertest would be the highest or lowest point of the quadratic equation. Your vertex would be (5,-9) because just look at x=4 and x=6, bit of the y values are -8 and when you look at x=3 and x=7 they are also the same because this is a quadratic equation.

Max or min: yours is a minimum because (5,-9) is the lowest point. Every value left and right of this are higher up the graph, so this would be a minimum.

*something that will help you see this all more clearly is if you graphed this or put it into Desmos to see the vertex etc.

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Alenkasestr [34]

So what are you trying to answer ?

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